An extension of Arnol'd's second stability theorem for the Euler equations

DOI10.1016/0167-2789(95)00312-6zbMath0890.58087OpenAlexW2050849470MaRDI QIDQ1917970

Michael Ghil, Gershon Wolansky

Publication date: 4 August 1996

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00312-6

zbMATH Keywords

Euler equationsfluid dynamicsenergy-Casimir functionalArnold's stabilityplanetary flows

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Stability theory for smooth dynamical systems (37C75)

Related Items (10)

Sobolev-like cones of trace-class operators on unbounded domains: interpolation inequalities and compactness properties ⋮ Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems ⋮ Relative equilibria in continuous stellar dynamics ⋮ Nonlinear stability of sinusoidal Euler flows on a flat two-torus ⋮ Stability criteria for the 2D \(\alpha\)-Euler equations ⋮ Compactness properties for trace-class operators and applications to quantum mechanics ⋮ Localized minimizers of flat rotating gravitational systems ⋮ On the unstable discrete spectrum of the linearized 2-D Euler equations in bounded domains ⋮ Stability of 2D steady Euler flows related to least energy solutions of the Lane-Emden equation ⋮ On the spectral instability and bifurcation of the 2D-quasi-geostrophic potential vorticity equation with a generalized Kolmogorov forcing

Cites Work

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• On nonlinear stability of polytropic galaxies
• Stability of quasi-geostrophic flow in a periodic channel
• Nonlinear stability of fluid and plasma equilibria
• An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems
• Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows
• On an apriori estimate in the theory of hydrodynamical stability

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